V-belt service life optimization design method based on particle swarm optimization

Abstract

The invention relates to a particle swarm algorithm-based V belt life optimization design method. The method comprises the following steps of constructing a life calculation model of a rubber V belt; the method comprises the following steps: inputting tensile strength, reference force elongation, hardness and elastic modulus of a V belt as samples by adopting a uniform test design method, and dividing into a training set, a verification set and a test set; obtaining a life prediction value by using a pre-established life calculation model; the maximum value of the service life of the V belt is used as an objective function, the tensile strength, the reference force elongation, the hardness and the elastic modulus of the V belt are used as parameters to be optimized, and the slip ratio and the tension failure threshold during dynamic operation of the V belt are used as constraint conditions. Compared with the traditional optimization of the volume and the size of the whole belt transmission system and the simple physical calculation optimization of the service life, the method has better global search capability and higher convergence speed for the optimization of multiple parameters, and has remarkable practical value and wide application prospect.

Description

Technical Field

[0001] The present invention relates to the field of product life optimization design, and more specifically to a V-belt life optimization design method based on particle swarm algorithm. Background Art

[0002] As the most widely used type of belt drive, rubber V-belt drive has been widely used in the field of mechanical power transmission due to its simple structure, smooth transmission, low cost, no need for lubrication, buffering and vibration absorption capabilities, and easy maintenance. Its main application scenarios include automotive transmission, agricultural machinery power transmission, wind turbine power generation, and large-scale engineering equipment, etc., occupying an extremely important position. However, in actual use, rubber V-belts will inevitably be worn and eventually break and fail. Therefore, optimizing the design of the life of the V-belt not only has important engineering value, but also can significantly improve its application efficiency and reliability.

[0003] Traditional V-belt optimization design mainly focuses on the goals of the entire transmission system, such as reducing the volume of the pulley, optimizing the center distance, and minimizing the number of belts. However, the optimization of V-belt performance and life often only stays on the analysis of a single factor, lacking a comprehensive consideration of the optimization parameters. This limitation easily leads to deviations and instability in the life optimization results, making it difficult to meet the design requirements for more efficiency and reliability. Summary of the invention

[0004] In view of the shortcomings of the prior art, the object of the present invention is to provide a V-belt life optimization design method based on particle swarm algorithm.

[0005] To achieve the above object, the present invention provides the following technical solution: a V-belt life optimization design method based on particle swarm algorithm, characterized in that it comprises the following steps:

[0006] Step 1: Establish a life prediction calculation model for the V-belt, collect physical property data and corresponding life to verify the model, and determine the parameters to be optimized as tensile strength, reference force elongation, hardness and elastic modulus and their upper and lower limits;

[0007] Step 2: For the physical parameters that need to be optimized, several levels are divided within the specified upper and lower limits, and the uniform experimental design method is used to obtain multiple groups of physical parameter combination schemes as input data, which are substituted into the V-belt life prediction calculation model established in step 1, and the life value of the V-belt is recorded as output data;

[0008] Step 3: Determine the number of input layers, hidden layers, output layers and the number of nodes in the hidden layer of the BP neural network, and establish a BP neural network model; randomly select 70% of the input data as training data, 15% as verification data, and 15% as test data from several groups of input data, and train and verify the BP neural network until the error meets the requirement of less than 5%;

[0009] Step 4: Use particle swarm algorithm to carry out optimization, take the maximum life of the V-belt as the optimization target, the tensile strength, reference force elongation, hardness and elastic modulus of the V-belt as the parameters to be optimized, and the upper and lower limits of the parameters to be optimized and the slip rate and tension force failure threshold of the V-belt during dynamic operation as the constraint conditions;

[0010] Step 5: Set the particle swarm algorithm parameters, write the program, and gradually iterate until convergence to obtain the optimal V-belt physical parameter combination scheme and the optimized V-belt life value.

[0011] As a further improvement of the present invention, the step 1 of establishing a life prediction calculation model for the V-belt and collecting physical property data and corresponding life to verify the model specifically includes:

[0012] Step 1, determine the type of V-belt, and then collect four physical parameters including tensile strength, reference force elongation, hardness and elastic modulus, as well as two dynamic time series parameters including slip rate and tension force;

[0013] Step 1 and 2: The four physical parameters and two dynamic time series parameters are respectively integrated into comprehensive features F1 and F2 using the SVR regression algorithm; the correlation between F1 and F2 is analyzed using the binary Copula function, and then the life prediction calculation model of the V-belt is constructed based on the binary Wiener process;

[0014] Step 13: Design a V-driven static test under standard working conditions to obtain the required test index data and verify the accuracy and effectiveness of the established life prediction calculation model.

[0015] As a further improvement of the present invention, the specific method of establishing the BP neural network model in step 3 is as follows: the V-belt tensile strength, reference force elongation, hardness and elastic modulus are used as the input layer of the BP neural network, the number of which is determined to be 4, and the output layer is the V-belt life, the number of which is determined to be 1; the hidden layer adopts a single hidden layer, and the calculation expression of the number of hidden layer nodes is:

[0016]

[0017] Among them, l is the number of nodes, m is the number of input layer nodes, and n is the number of output layer nodes. After calculation, the number of hidden layer nodes is finally determined to be 10. Based on the determined basic model parameters, the BP neural network model of the V-belt is established with the help of MATLAB.

[0018] As a further improvement of the present invention, the life prediction calculation model of the V-belt is constructed as follows:

[0019]

[0020] Where k = 1, 2; w 1 is the failure threshold of the physical property fusion feature F1, w 2 is the failure threshold of the dynamic time series feature F2, and the corresponding parameter of feature F1 (μ 1 ,σ 1 ), feature F2 corresponds to parameter (μ 2 ,σ 2 );f 1RUL (t), f 2RUL (t) are their respective marginal distribution functions, c(F 1 (t),F 2 (t); θ) is the probability density function corresponding to the selected binary Copula function; f RUL (t|w k ,μ k ,σ k ,θ) is the probability density distribution function of the V-belt life, and the time corresponding to the maximum function value is the predicted calculated value of the V-belt life.

[0021] As a further improvement of the present invention, the constraint conditions in step 4 are specifically as follows:

[0022]

[0023] Among them, tensile strength is σ, reference force elongation is ξ, hardness is H, and elastic modulus is E.

[0024] As a further improvement of the present invention, in step five, the particle swarm algorithm parameters are set, a program is written, and it is gradually iterated until convergence to obtain the optimal V-belt physical parameter combination scheme and the optimized V-belt life value in the following specific manner: first, the particle swarm is initialized, and then the particle fitness is calculated as the optimized life value of the V-belt in combination with the established BP neural network model, and the particle speed and position are continuously updated to obtain the fitness extreme value; finally, the PSO optimization solution is performed to obtain the result, which includes tensile strength, reference force elongation, elastic modulus, and hardness, and finally converges after multiple iterations to reach the optimal value of the V-belt life.

[0025] Beneficial effects of the present invention:

[0026] The influence of multiple factors on the life of V-belt static performance and dynamic operation fatigue index is comprehensively analyzed, and a V-belt life prediction calculation model with more accurate prediction performance is constructed. Then, the parameters to be optimized are comprehensively considered, the dynamic failure index and threshold of the V-belt are determined, and the maximum life of the V-belt is taken as the optimization goal. The BP neural network combined with the particle swarm algorithm is used to obtain the optimal combination of parameters to be optimized, so as to optimize the life of the V-belt.

[0027] The theoretical basis model of the present invention has high accuracy and strong robustness, and adopts a combination of a neural network proxy model and a particle swarm optimization algorithm, which has better global search capabilities and greatly improves the optimization efficiency and accuracy. It can provide a basic reference for the life improvement research in the V-belt transmission industry, and has important theoretical significance and engineering application value for improving the efficiency and service life of V-belt transmissions and achieving high reliability of mechanical transmission systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 is a flow chart of the present invention;

[0029] Figure 2 It is the probability density distribution diagram of the V-belt life prediction model, and the maximum value corresponds to the V-belt life value;

[0030] Figure 3 This is a comparison chart of the prediction accuracy verification results of the V-belt life prediction model;

[0031] Figure 4 This is the result diagram of BP neural network model training and verification;

[0032] Figure 5 This is a graph showing the optimization iterative results of the BP neural network combined with the PSO particle swarm algorithm. DETAILED DESCRIPTION

[0033] The present invention will be further described below in detail with reference to the embodiments shown in the accompanying drawings.

[0034] Reference Figures 1 to 5 As shown, a V-belt life optimization design method based on a particle swarm algorithm in this embodiment includes the following steps:

[0035] S1. Establish a life prediction calculation model for V-belts, collect physical property data and corresponding life to verify the model, and ensure that the accuracy of the calculation model is above 95%; determine the parameters to be optimized as tensile strength, reference force elongation, hardness and elastic modulus and their upper and lower limits;

[0036] The specific implementation of the above steps includes the following sub-steps:

[0037] S11. Determine the B-type V-belt with a length of 1499mm as the research object, design dynamic and static tests under the conditions of Zhejiang manufacturing standard "T / ZZB 0060-2016 Ordinary V-belt for Transmission", collect pre-processed test data,

[0038] Then the nonlinear mapping relationship between the physical parameters of the V-belt, such as tensile strength, reference force elongation, hardness and elastic modulus, and the lifespan is explored; and the relationship between the slip rate and tension force of the V-belts of the same batch of products and the lifespan under dynamic timing conditions is analyzed and summarized;

[0039] S12. The four physical parameters and two dynamic time series parameters are fused into comprehensive features F1 and F2 respectively by using SVR regression algorithm; the correlation between F1 and F2 is analyzed by binary Copula function, and then the life prediction calculation model of V-belt is constructed based on binary Wiener process;

[0040] The specific implementation method is as follows: the SVR regression algorithm is used to calculate the weight factors of the physical property and dynamic time series characteristic models, and then the four physical property parameters and two dynamic time series parameters are respectively integrated into comprehensive features F1 and F2, and the corresponding V-belt fatigue failure threshold is determined; the binary Frank Copula function is selected according to the AIC information criterion to analyze the correlation between F1 and F2, and then the life prediction calculation model of the V-belt is constructed based on the binary Wiener process, that is, the life probability density distribution function expression of the V-belt is as follows:

[0041]

[0042] where k = 1, 2; w 1 is the failure threshold of the physical property fusion feature F1, w 2 is the failure threshold of the dynamic time series feature F2, and the corresponding parameter of feature F1 (μ 1 ,σ 1 ), feature F2 corresponds to parameter (μ 2 ,σ 2 );f 1RUL (t), f 2RUL (t) are their respective marginal distribution functions, c(F 1 (t),F 2 (t); θ) is the probability density function corresponding to the selected binary Copula function; f RUL (t|w k ,μ k ,σ k ,θ) is the probability density distribution function of the V-belt life, and the time corresponding to the maximum value of the function is the predicted value of the V-belt life (see Appendix Figure 2 shown).

[0043] S13. Design a V-drive static test under standard working conditions to obtain the required test index data and verify the accuracy and effectiveness of the established life prediction calculation model.

[0044] The specific implementation method is: design a V-belt static test under the working conditions of Zhejiang manufacturing standard "T / ZZB 0060-2016 Ordinary V-belts for Transmission", obtain the required test index data, use the maximum likelihood function method to estimate the unknown parameters at 15h as the unit time point, obtain the life prediction calculation value, compare it with the V-belt life value recorded in the test, and finally verify that the accuracy of the established life prediction calculation model is above 95% (as shown in the attached Figure 3 This laid a theoretical foundation for subsequent calculations.

[0045] Taking B-type V-belt as the research object, the physical parameters to be optimized and their upper and lower limits are determined as follows: tensile strength is [5.0, 10.0] KN, reference force elongation is (0, 0.07), hardness is [78, 83] and elastic modulus is (69, 100) MPA.

[0046] S2. For the physical parameters that need to be optimized, several levels are divided within the specified upper and lower limits. The uniform experimental design method is used to obtain multiple groups of physical parameter combination schemes as input data, which are substituted into the V-belt life prediction calculation model to obtain the V-belt life value as output data;

[0047] The specific implementation method is: the tensile strength, reference force elongation, hardness and elastic modulus of the V-belt are divided into 10 levels within the upper and lower limit ranges (as shown in Table 1), and the uniform experimental design method is adopted to obtain 40 groups of physical property parameter combination schemes, and the life value is calculated based on the established V-belt life prediction model.

[0048] Table 1

[0049]

[0050]

[0051] S3. Determine the number of input layers, hidden layers, output layers and the number of nodes in the hidden layer of the BP neural network, and establish a BP neural network model; randomly select 70% of the input data as training data, 15% as verification data, and 15% as test data from several groups of input data, and train and verify the BP neural network until the error meets the requirement of less than 5%;

[0052] The specific implementation method is as follows: the input layer of the BP neural network is the four parameters to be optimized, and the number is determined to be 4; the output layer is the V-belt life, and the number is determined to be 1; in order not to waste resources and improve optimization efficiency, the hidden layer adopts a single-layer structure, and the number of hidden layer nodes is determined to be 10. The BP neural network model is constructed with the help of MATLAB's neural network toolbox. The 40 groups of schemes obtained by the uniform experimental design are randomly divided into 70%, 15%, and 15% distributions as training, verification, and test sets, and finally the BP neural network model of the V-belt is established and verified to achieve excellent prediction accuracy (as shown in the attached figure). Figure 4 shown).

[0053] S4. The particle swarm algorithm is used to optimize the V-belt, taking the optimal life value of the V-belt as the optimization target, the tensile strength, reference force elongation, hardness and elastic modulus of the V-belt as the parameters to be optimized, and the upper and lower limits of the parameters to be optimized and the slip rate η and tension force F failure threshold of the V-belt during dynamic operation as the constraints;

[0054] The specific implementation method is: combining the BP neural network model with the particle swarm optimization algorithm (PSO), determining the parameters to be optimized for the V-belt as tensile strength σ, reference force elongation ξ, hardness H and elastic modulus E, and the optimization constraints are as follows:

[0055]

[0056] S5. Set the particle swarm algorithm parameters, write a program, and gradually iterate until convergence to obtain the optimal V-belt physical parameter combination scheme and the optimized V-belt life value.

[0057] The specific implementation method is as follows: complete the subroutine writing of fitness function and constraint conditions in MATLAB, and set the population size to 100, the maximum evolutionary generation to 50 generations, first initialize the particle swarm, and then combine the established BP neural network model to calculate the particle fitness, which is the optimized life value of the V-belt, and continuously update the particle speed and position to obtain the fitness extreme value; finally, perform PSO optimization and solve the calculation results to obtain the following results: tensile strength is 10KN, reference force elongation is 4.256%, elastic modulus is 70.0593MPA, hardness is 78, and finally iterates 26 times and converges to achieve the optimal value of V-belt life of 272.056h (as shown in the attached figure). Figure 5 As shown in the figure, compared with the life of the V-belt before optimization, the life of the V-belt is increased by 13.4%, which verifies that the optimization method is effective and practical.

[0058] The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should also be regarded as the protection scope of the present invention.

Claims

1. A V-belt life optimization design method based on particle swarm algorithm, characterized by: The steps include: Step 1: Establish a life prediction calculation model for the V-belt, collect physical property data and corresponding life to verify the model, and determine the parameters to be optimized as tensile strength, reference force elongation, hardness and elastic modulus and their upper and lower limits; Step 2: For the physical parameters that need to be optimized, several levels are divided within the specified upper and lower limits, and the uniform experimental design method is used to obtain multiple groups of physical parameter combination schemes as input data, which are substituted into the V-belt life prediction calculation model established in step 1, and the life value of the V-belt is recorded as output data; Step 3: Determine the number of input layers, hidden layers, output layers and the number of nodes in the hidden layer of the BP neural network, and establish a BP neural network model; randomly select 70% of the input data as training data, 15% as verification data, and 15% as test data from several groups of input data, and train and verify the BP neural network until the error meets the requirement of less than 5%; Step 4: Use particle swarm algorithm to carry out optimization, take the maximum life of the V-belt as the optimization target, the tensile strength, reference force elongation, hardness and elastic modulus of the V-belt as the parameters to be optimized, and the upper and lower limits of the parameters to be optimized and the slip rate and tension force failure threshold of the V-belt during dynamic operation as the constraint conditions; Step 5: Set the particle swarm algorithm parameters, write the program, and gradually iterate until convergence to obtain the optimal V-belt physical parameter combination scheme and the optimized V-belt life value.

2. The V-belt life optimization design method based on particle swarm algorithm according to claim 1 is characterized in that: The step 1 of establishing a life prediction calculation model for the V-belt and collecting physical property data and corresponding life to verify the model specifically includes: Step 1, determine the type of V-belt, and then collect four physical parameters including tensile strength, reference force elongation, hardness and elastic modulus, as well as two dynamic time series parameters including slip rate and tension force; Step 1 and 2: The four physical parameters and two dynamic time series parameters are respectively integrated into comprehensive features F1 and F2 using the SVR regression algorithm; the correlation between F1 and F2 is analyzed using the binary Copula function, and then the life prediction calculation model of the V-belt is constructed based on the binary Wiener process; Step 13: Design a V-driven static test under standard working conditions to obtain the required test index data and verify the accuracy and effectiveness of the established life prediction calculation model.

3. The V-belt life optimization design method based on particle swarm algorithm according to claim 1 or 2, characterized in that: The specific method of establishing the BP neural network model in step 3 is as follows: The tensile strength, reference force elongation, hardness and elastic modulus of the V-belt are used as the input layer of the BP neural network, and the number is determined to be 4. The output layer is the life of the V-belt, and the number is determined to be 1. The hidden layer uses a single hidden layer, and the calculation expression of the number of hidden layer nodes is: Among them, l is the number of nodes, m is the number of input layer nodes, and n is the number of output layer nodes. After calculation, the number of hidden layer nodes is finally determined to be 10. Based on the determined basic model parameters, the BP neural network model of the V-belt is established with the help of MATLAB.

4. The V-belt life optimization design method based on particle swarm algorithm according to claim 2 is characterized in that: The life prediction calculation model of the V-belt is constructed as follows: Where, k = 1, 2; w1 is the failure threshold of the physical property fusion feature F1, w2 is the failure threshold of the dynamic time series feature F2, feature F1 corresponds to parameters (μ1, σ1), feature F2 corresponds to parameters (μ2, σ2); f 1RUL (t), f 2RUL (t) are their respective marginal distribution functions, c(F1(t), F2(t); θ) is the probability density function corresponding to the selected binary Copula function; f RUL (tw k ,μ k ,σ k ,θ) is the probability density distribution function of the V-belt life, and the time corresponding to the maximum function value is the predicted calculated value of the V-belt life.

5. The V-belt life optimization design method based on particle swarm algorithm according to claim 1 or 2, characterized in that: The constraints in step 4 are as follows: Among them, tensile strength is σ, reference force elongation is ξ, hardness is H, and elastic modulus is E.

6. The V-belt life optimization design method based on particle swarm algorithm according to claim 1 or 2, characterized in that: In the step 5, the particle swarm algorithm parameters are set, a program is written, and it is gradually iterated until convergence to obtain the optimal V-belt physical parameter combination scheme and the optimized V-belt life value. The specific method is as follows: first, the particle swarm is initialized, and then the particle fitness is calculated as the optimized life value of the V-belt in combination with the established BP neural network model, and the particle speed and position are continuously updated to obtain the fitness extreme value; finally, the PSO optimization solution is performed to obtain the result, which includes tensile strength, reference force elongation, elastic modulus, and hardness. Finally, after multiple iterations, it converges to reach the optimal value of the V-belt life.

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